Weighted Multiple Regression Estimation for Survey Model Sampling

by James R. Knaub, Jr.

Abstract:
Model-based inference has performed well for electric power establishment survey
data at the Energy Information Administration (EIA), using weighted, simple linear regression, as
pioneered by K.R.W. Brewer, R.M. Royall, and others. Cutoff sampling is used because it is not
practical to collect frequently from among the smallest members of these highly skewed
distributions, where nonsampling error and respondent burden can be particularly serious
problems. Further, certain generation and sales for resale data have proved to be relatively
difficult candidates for sampling. A weighted, multiple linear regression model, using a cutoff
sample, where one regressor is the data element of interest as captured in a previous census, and
another regressor is the nameplate capacity of the generating entity, has proved to be extremely
valuable. This has been applied to monthly sampling, where regressor data have come from
previous annual census information. Estimates of totals, with their corresponding estimates of
variance, have been greatly improved by this methodology. Heteroscedasticity with respect to
each regressor is addressed.